A seismic survey represents an attempt to image or map the subsurface of the earth by sending sound energy down into the ground and recording the “echoes” that return from the rock layers below. The source of the down-going sound energy might come, for example, from explosions or seismic vibrators on land, or air guns in marine environments. During a seismic survey, the energy source is positioned at various locations near the surface of the earth above a geologic structure of interest. Each time the source is activated, it generates a seismic signal that travels downward through the earth, is reflected or transmitted, and, upon its return, is recorded at a great many locations on the surface. Multiple source/recording combinations are then combined to create a near continuous profile of the subsurface that can extend for many miles. In a two-dimensional (2D) seismic survey, the recording locations are generally laid out along a single line, whereas in a three dimensional (3D) survey the recording locations are distributed across the surface, sometimes as a series of closely spaced adjacent two-dimensional lines and in other cases as a grid of source and receiver lines that are arranged to be at some other angle with respect to each other. In simplest terms, a 2D seismic line can be thought of as giving a cross sectional picture (vertical slice) of the earth layers as they exist directly beneath the recording locations. A 3D survey produces a data “cube” or volume that is, at least conceptually, a 3D picture of the subsurface that lies beneath the survey area. In reality, though, both 2D and 3D surveys interrogate some volume of earth lying beneath the area covered by the survey.
A seismic survey is composed of a very large number of individual seismic recordings or traces. In a typical 2D survey, there will usually be several tens of thousands of traces, whereas in a 3D survey the number of individual traces may run into the multiple millions of traces. (Chapter 1, pages 9-89, of Seismic Data Processing by Ozdogan Yilmaz, Society of Exploration Geophysicists, 1987, contains general information relating to conventional 2D processing and that disclosure is incorporated herein by reference. General background information pertaining to 3D data acquisition and processing may be found in Chapter 6, pages 384-427, of Yilmaz, the disclosure of which is also incorporated herein by reference.
A seismic trace is a digital recording of the acoustic energy reflecting from inhomogeneities or discontinuities in the subsurface, a partial reflection occurring each time there is a change in the elastic properties of the subsurface materials. The digital samples are usually acquired at 0.002 second (2 millisecond or “ms”) intervals, although 4 millisecond and 1 millisecond sampling intervals are also common. Each discrete sample in a conventional digital seismic trace is associated with a travel time, and in the case of reflected energy, a two-way travel time from the source to the reflector and back to the surface again, assuming, of course, that the source and receiver are both located on the surface. Many variations of the conventional source-receiver arrangement are used in practice, e.g. VSP (vertical seismic profiles) surveys, ocean bottom surveys, etc. Further, the surface location of every trace in a seismic survey is carefully tracked and is generally made a part of the trace itself (as part of the trace header information). This allows the seismic information contained within the traces to be later correlated with specific surface and subsurface locations, thereby providing a means for posting and contouring seismic data—and attributes extracted therefrom—on a map (i.e., “mapping”).
The data in a 3D survey are amenable to viewing in a number of different ways. First, horizontal “constant time slices” may be taken extracted from a stacked or unstacked seismic volume by collecting all of the digital samples that occur at the same travel time. This operation results in a horizontal 2D plane of seismic data. By animating a series of 2D planes it is possible for the interpreter to pan through the volume, giving the impression that successive layers are being stripped away so that the information that lies underneath may be observed. Similarly, a vertical plane of seismic data may be taken at an arbitrary azimuth through the volume by collecting and displaying the seismic traces that lie along a particular line. This operation, in effect, extracts an individual 2D seismic line from within the 3D data volume.
Seismic data that have been properly acquired and processed can provide a wealth of information to the explorationist, one of the individuals within an oil company whose job it is to locate potential drilling sites. For example, a seismic profile gives the explorationist a broad view of the subsurface structure of the rock layers and often reveals important features associated with the entrapment and storage of hydrocarbons such as faults, folds, anticlines, unconformities, and sub-surface salt domes and reefs, among many others. During the computer processing of seismic data, estimates of subsurface rock velocities are routinely generated and near surface inhomogeneities are detected and displayed. In some cases, seismic data can be used to directly estimate rock porosity, water saturation, and hydrocarbon content. Less obviously, seismic waveform attributes such as phase, peak amplitude, peak-to-trough ratio, and a host of others, can often be empirically correlated with known hydrocarbon occurrences and that correlation applied to seismic data collected over new exploration targets.
Of course, the ultimate goal is to obtain a clear and undistorted image of the subsurface. To that end, there has been—and continues to be—ongoing research that is aimed at mathematically transforming a seismic section or volume into a true earth model that is consistent with the observed data. One of the more promising, if computationally intensive, approaches has been full waveform seismic waveform inversion. Broadly speaking, the “inverse problem” attempts to estimate physical properties of the Earth from the recorded seismic data. Such model properties might include 2D or 3D subsurface velocities, densities, etc., wherein the model parameters are to be estimated at each point of a subsurface grid or volume. In most approaches, an iterative procedure is utilized wherein the current subsurface model is used to generate a synthetic seismic data set. The model is then updated as a function of the difference between the recorded seismic data and the synthetic data set.
Of particular interest for purposes of the instant invention, frequency-domain waveform inversion is a technique that has been suggested as a way to determine the subsurface velocities from seismic data. Those of ordinary skill in the art will recognize that this method traditionally requires the computation of frequency domain wave fields using forward modeling. However, because of the computational difficulties involved with solving the 3D frequency domain forward modeling problem, applications to synthetic and field data have been largely limited to 2D implementations. What is needed, of course, is a method of frequency-domain waveform inversion that can be applied to both 2D and 3D data.
The following publications, each incorporated herein by reference as if fully set out at this point, are examples of prior art approaches to wave field inversion.                S. Operto, C. Ravaut, L. Improta, J. Virieux, A. Herrero and P. Dell'Aversana, Quantitative imaging of complex structures from dense wide-aperture seismic data by multiscale traveltime and waveform inversions: a case study. Geophysical Prospecting, 52, 625-651, 2004,        Pica, A., Diet, J., and Tarantola, A., 1990, Nonlinear inversion of seismic reflection data in a laterally invariant medium: Geophysics, 55, no. 03, 284-292.        Pratt, R. G., Song, Z.-M., Williamson, P., and Warner, M., 1996, Two-dimensional velocity models from wide-angle seismic data by wavefield inversion: Geophys. J. Int., 124, 323-340.        Shipp, R. M., and Singh, S. C., 2002, Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data: Geophys. J. Int., 151, 325-344.        Sirgue, L. and Pratt, R. G., 2004, Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies: Geophysics, Soc. of Expl. Geophys., 69, 231-248.        Song, Z. M., Williamson, P. R., and Pratt, R. G., 1995, Frequency-domain acoustic-wave modeling and inversion of crosshole data: Part ii: Inversion method, synthetic experiments and real-data results: Geophysics, 60, no. 03, 796-809.        Tarantola, A., 1984a, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, no. 08, 1259-1266.        
Heretofore, as is well known in the seismic processing and seismic interpretation arts, there has been a need for a computationally efficient method of waveform inversion that can be applied to both 2D and 3D data sets. Accordingly, it should now be recognized, as was recognized by the present inventor, that there exists, and has existed for some time, a very real need for a method of seismic data processing that would address and solve the above-described problems.
Before proceeding to a description of the present invention, however, it should be noted and remembered that the description of the invention which follows, together with the accompanying drawings, should not be construed as limiting the invention to the examples (or preferred embodiments) shown and described. This is so because those skilled in the art to which the invention pertains will be able to devise other forms of this invention within the ambit of the appended claims.